Abstract
The theory of sound propagation through a bank of rigid parallel tubes in the presence of a nominally steady, low Mach number cross flow is discussed. A detailed diffraction analysis is given for the idealized but mathematically tractable case of a bank of strips set at zero angle of attack to the mean flow. Various approximations for the dispersion equation governing the propagation of long waves are derived, including the influence of acoustically induced vortex shedding from the strip trailing edges and of hydrodynamic interactions between neighbouring strips. The sound is attenuated by a transfer of energy to the kinetic energy of the essentially incompressible field of the shed vorticity. It is shown how the principle of conservation of energy and a Kramers-Kronig dispersion relation can be combined to yield an alternative derivation of the dispersion equation. This procedure is applicable to a simplified model of propagation through a bank of rigid tubes of circular cross section, and an approximation to the dispersion equation is obtained in this case. The relevance of these results to bound resonances in tube bank cavities is discussed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
